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Simplifying 154x2 + -108x + 16 = 0 Reorder the terms: 16 + -108x + 154x2 = 0 Solving 16 + -108x + 154x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(8 + -54x + 77x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + -54x + 77x2)' equal to zero and attempt to solve: Simplifying 8 + -54x + 77x2 = 0 Solving 8 + -54x + 77x2 = 0 Begin completing the square. Divide all terms by 77 the coefficient of the squared term: Divide each side by '77'. 0.1038961039 + -0.7012987013x + x2 = 0 Move the constant term to the right: Add '-0.1038961039' to each side of the equation. 0.1038961039 + -0.7012987013x + -0.1038961039 + x2 = 0 + -0.1038961039 Reorder the terms: 0.1038961039 + -0.1038961039 + -0.7012987013x + x2 = 0 + -0.1038961039 Combine like terms: 0.1038961039 + -0.1038961039 = 0.0000000000 0.0000000000 + -0.7012987013x + x2 = 0 + -0.1038961039 -0.7012987013x + x2 = 0 + -0.1038961039 Combine like terms: 0 + -0.1038961039 = -0.1038961039 -0.7012987013x + x2 = -0.1038961039 The x term is -0.7012987013x. Take half its coefficient (-0.3506493507). Square it (0.1229549671) and add it to both sides. Add '0.1229549671' to each side of the equation. -0.7012987013x + 0.1229549671 + x2 = -0.1038961039 + 0.1229549671 Reorder the terms: 0.1229549671 + -0.7012987013x + x2 = -0.1038961039 + 0.1229549671 Combine like terms: -0.1038961039 + 0.1229549671 = 0.0190588632 0.1229549671 + -0.7012987013x + x2 = 0.0190588632 Factor a perfect square on the left side: (x + -0.3506493507)(x + -0.3506493507) = 0.0190588632 Calculate the square root of the right side: 0.138053842 Break this problem into two subproblems by setting (x + -0.3506493507) equal to 0.138053842 and -0.138053842.Subproblem 1
x + -0.3506493507 = 0.138053842 Simplifying x + -0.3506493507 = 0.138053842 Reorder the terms: -0.3506493507 + x = 0.138053842 Solving -0.3506493507 + x = 0.138053842 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3506493507' to each side of the equation. -0.3506493507 + 0.3506493507 + x = 0.138053842 + 0.3506493507 Combine like terms: -0.3506493507 + 0.3506493507 = 0.0000000000 0.0000000000 + x = 0.138053842 + 0.3506493507 x = 0.138053842 + 0.3506493507 Combine like terms: 0.138053842 + 0.3506493507 = 0.4887031927 x = 0.4887031927 Simplifying x = 0.4887031927Subproblem 2
x + -0.3506493507 = -0.138053842 Simplifying x + -0.3506493507 = -0.138053842 Reorder the terms: -0.3506493507 + x = -0.138053842 Solving -0.3506493507 + x = -0.138053842 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3506493507' to each side of the equation. -0.3506493507 + 0.3506493507 + x = -0.138053842 + 0.3506493507 Combine like terms: -0.3506493507 + 0.3506493507 = 0.0000000000 0.0000000000 + x = -0.138053842 + 0.3506493507 x = -0.138053842 + 0.3506493507 Combine like terms: -0.138053842 + 0.3506493507 = 0.2125955087 x = 0.2125955087 Simplifying x = 0.2125955087Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4887031927, 0.2125955087}Solution
x = {0.4887031927, 0.2125955087}
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